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Simulation and Modeling of Large Microwave and Millimeter-Wave Systems, Part 1

Michael Steer with Nikhil Kriplani, Carlos Christofferson and Shivam Priyadarshi

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Copyright 2009 to 2011 by M. Steer, N. Kriplani and S. Priyadarshi Not to be posted on the web or distributed electronically without permission.

http://www.freeda.org

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Outline Multi-Physics Simulator (fREEDATM) Minimizes Energy Error (not KCL) Time-domain EM interface Frequency-domain EM (network parameter interface) Thermal, Noise Photonics, Mechanical Molecular Electronics

Code reuse: Uses Trilinos Numerical Libraries from Los Alamos

Simple device modeling Transient Simulation Uncompromised commitment to accuracy Circuit/Field Interaction

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fREEDA

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Open Source / Open Licensing BSD License (Open to companies to do what they want), well almost there.

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Essential Concepts for Multi-Physics Modeling • Integration of multi physics problem into the circuit

modeling domain • Object Oriented Approach • Global Modeling

– EM Interconnect Modeling – Digital Macromodeling – Opto Electronic Modeling – Quantum Modeling – Molecular Modeling – Materials Modeling – Bio / Chemical Modeling

• Interfaces

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Universal Error Concept (Energy Norm)

Universal error concept: AT A TERMINAL Σ FLUX = 0 All Potentials are the SAME

MECHANICAL

THERMAL

ELECTRICAL

FORCE

HEAT CURRENT

I

Flow

POSITION

TEMPERATURE

V

Effort

INERTIAL REFERENCE FRAME

ABSOLUTE ZERO

LOCAL GROUND

LOCAL REFERENCE NODE

For each state variable x there must be a flow and an effort contribution.

i(t) v(t)

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Many Unique Models

• EM Interface (TD and FD) • Electro-Thermal • Dynamic Range • Time Delay • Large Signal Noise • Electro-Optic • Molecular Diode

n+ poly

STI STI

tox

Vg

oxide

L

p type

Jg (tunneling)

V_ref

MOSCAP World’s first implementation

E.G. The tunnel process cannot be expressed as a current-charge-voltage expression as Spice requires. Instead use state variables to implement tunneling correctly.

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Circuit Theory

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Background Reading

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Background Reading

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Microstrip Model In a Field Simulator Voltages Are Determined By

Integrating The Electric Field Along a Path In Microstrip Problems the Field is Integrated Over

The Paths Shown to Obtain V The Path of Integration Matters The Dashed Path Yields a Different Value of V2

V 1

V 2

Not the same point electrically.

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Microstrip Model

Network Model: 11 12

21 22

S SS S

V1 V2 REF REF

REF REF

V2 V1

But a (SPICE) Circuit does not have two reference terminals.

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Global Reference Node

• Perfect Ground Plane Assumed • (No Retardation Effects) • In A Field Simulator Voltages Are Determined By

Integrating The Electric Field Along a Path • In Microstrip Problems the Field is Integrated

Over The Paths Shown to Obtain • The Path of Integration Matters • The Dashed Path Yields a Totally Different

Value • of

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Conventional Microwave Circuits (e.g. Microstrip)

V 1

V 2

V and 1

V 2

V 2

Current Microwave Simulators (Linear, Harmonic Balance, Transient) are Based on Nodal Voltage Descriptions To Use Nodal Voltages There Must Be a Common Reference Node Field Simulators Currently Require A Common Reference Ground

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Local reference node concept • This avoids non-physical connections and therefore is

fundamental for the analysis of spatially distributed circuits as well as for simultaneous thermal-electrical simulations.

V1 V2 REF REF

LOCAL REFERENCE TERMINAL

How to extend this beyond two terminal ports?

Our common view of a port is that it has two terminals

i1

i1

i2

i2

1 2

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Non- fREEDA fREEDA

Circuit Circuit

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Circuit vs. Network Graph

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Circuit Graph

Network Graph

Concept of Spice

CIRCUIT GRAPH

NETWORK GRAPH Concept of fREEDA

Must use two circuit graphs to represent a general circuit

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Network Graph

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A

N

U

T S

R Q

P

O

F

L

G

H

I B

C J

D

K E

A node a edge a

b

Information is stored in fREEDA as a Network Graph but the difference between a terminal and an element is retained.

c

d

e

f

A

B

C

D

E

F

G

H

I

J

L

M

K

N

O

P

Q R

S

T

U

a b

c

d

e f

h g

g h

NETWORK GRAPH

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Modeling Concept

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SPATIALLY DISTRIBUTED CIRCUIT

LINEAR CIRCUIT

NONLINEAR NETWORK

THERMAL NETWORK

LINEAR NETWORK

• Nonlinear Analysis Must be Point of Integration Use SPICE-like & HARMONIC BALANCE analyses

• Use Existing Domain Specific Analyses E.G. Thermal, Field • Behavioral Modeling Is the Key to Using Results of One Simulator In Another

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Modeling Scope

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Can handle

11

2 32 31 12 2 3 3

1 1 1

( )( )( ), , ( ), , , ,

( ) ( )( ) ( )( ) , , , , , ,

( ), , ( )

nn

n n

n

dx tdx tx t x t

dt dtd x t d x td x t d x t

y t Fdt dt dt dt

x t x tτ τ

= − −

Where y(t) is either an i(t) or a v(t). Also in any type of analysis we want dy/dx The exact derivatives (w.r.t. time or frequency etc.) we want depend on the type of analysis we are doing (transient, wavelet, harmonic balance). The derivatives needed are calculated using ADOL-C under control of the analysis routines. This is why the same model can be used in any type of analysis.

ADOL-C is one of the many support libraries.

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fREEDA Unique Feature: Nonlinear devices models based on

state variables: • This provides great flexibility for

the design of new models. All of the analyses are state-variable-based, including a time marching analysis (different integration methods available) and a unique wavelet transient analysis.

• The state variables can be chosen to achieve robust numerical characteristics.

• The calculation of derivatives are free of truncation errors at a small multiple of the run time required to evaluate the original function with little additional memory required. (ADOLC)

CONVENTIONAL DIODE MODEL

STRONG NONLINEARITY v

i

v

x

x

NEW

NEW

MODERATE NONLINEARITY

+

i x

v =

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Bottom DBR

Top DBR

p-contact

Oxide

Light Output

Active Region n-contact

VCSEL Modeling

Single Mode Rate Equations Carrier density dN(t)/dt =ηi(I(t)-IL(T))/τ – N(t)/τnr – G(T)(N(t)-N0(T))S(t)/(1+εS(t)) Photon density dS(t)/dt = -S(t)/τp + βN(t)/τr + G(T)(N(t)-N0(T))S(t)/(1+εS(t)) Temperature dT(t)/dt = -T(t)/τth + (T0+(I(t)V(t)-P0(t))Rth)/τth

Leakage Current

IL = IL0exp[(-a0+ a1N0 + a2N0T- a3/N0)/T]

Temperature dependence of Gain and Transparency

G(T) = G0(ag0 + ag1T +ag2T2) / (bg0 + bg1T +bg2T2)

N0(T) = Nt0(cn0+cn1T+cn2T2)

Transim Power vs Current

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

3.00E-03

3.50E-03

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

Current(amps)

Pow

er(w

atts

)

Power@298K

Power@323K

Power@338KLeakage @298K

Leak

age

(mA

)

0

10

20

30

Transient Optical Output Power

Time(10ns)

drive current

Time(ns)

Wavelength Chirp

DC Optical Power versus Drive Current

Rollover from leakage

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Power and Wavelength degradation due to two components

Electro-Optics

Optical Power Wavelength z=12m z=12m

m

f1=12mm, R=0.04 f2=12mm, R=0.04

Detector

Lens2 Lens1

Vcsel

No feedback

L1 feedback

L1+L2 feedback

No feedback

L1 feedback

L1+L2 feedback

Output power degradation due

to single and double lens feedback

Output wavelength degradation due

to single and double lens feedback

With: Mark Niefeld Ravi Pant Univ. of Arizona

Feedback Results:

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Time Delays

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Spice handles only short (< 4 time step) time delays.

TWTA used to validated fREEDA’s ability to handle models with long time delays. Also implemented in many transistor models.

100

101

102

103

104

100

101

102

103

104

Specified delay (ns)

Obs

erve

d de

lay

(ns)

0 2000 4000 6000 8000 10000 12000 14000-1

-0.5

0

0.5

1

Time (ps)

Inpu

t Ter

min

al V

olta

ge (v

olts

)

0 2000 4000 6000 8000 10000 12000 14000-3

-2

-1

0

1

2

3

Time (ps)

Out

put T

erm

inal

Vol

tage

(vol

ts)

fREEDA has no limit

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Transient Simulation

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Choice of Time Step to keep error below a set tolerance.

Conventional approach

Result obtained with linear extrapolation

Result from nonlinear iteration (Trapezoidal / Backward Euler)

Tn+1 Tn Tn-1

Error estimate

Poor estimate of error leads to inappropriate choice of time step

Conventional Time Stepping Algorithm

IDEAL RESULT

The difference between the nonlinear iteration and the straight line extrapolation is taken as an estimate of error. If the error is too large the time step is reduced by a factor of 2. If the error is very low the time step is increased by A factor of 2. This results in excessively short time steps around curves and limits dynamic range.

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fREEDA Time Stepping Algorithm

New approach

Error estimate

Tn+1 Tn Tn-1 Better estimate of error leads to a better choice of time step

Result from

Backward Euler

Result from trapezoidal IDEAL

RESULT

The difference between the Backward Euler and trapezoidal estimates is an incredibly good estimate of error. If the error is too large the time step is reduced by a factor of 2. If the error is very low the time step is increased by A factor of 2. The half way point is taken as the answer.

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26 -120 -110 -100 -90 -80 -70 -60 -50 -40 -30 -20

-250

-200

-150

-100

-50

0

Input Power at 11GHz(dB)Out

put P

ower

(dB

) at

the

third

ord

er in

term

odul

atio

n pr

oduc

ts

fREEDA-12GHzfREEDA-9GHz ADS-12GHz ADS-9GHz Linear-12GHzMeasured Measured

Fundamental Frequency, f1 = 10GHz, P(f1) = -20dBSecond Tone, f2 = 11GHz

OUTPUT POWER OF TOIAT 9 GHz

OUTPUT POWER OF TOIAT 12 GHz

Spectrum Analyzer Noise Floor

Performs better than Traditional HB simulators

160 dB dynamic range with better than 0.5 dB accuracy.

Excellent agreement with measurements

FEATURES: •High Dynamic Range PHEMT 2-stage Low Noise Amplifier. •8.5 GHz to 14 GHz Frequency Band. •18dB Gain. •+6 V Supply Voltage. •2dB Noise Figure. •Can be used as pre-driver amplifier for phased array radar as well as commercial communications applications.

Two-Tone Test of Dynamic Range (X-Band Amplifier)

LMA411

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0 Tolerance

0.002 0.004 0.006 0.008 0.01

Error

0.01

0.02

0

0.03

0.04

0.05

CONVENTIONAL

NEW

High Dynamic Range Through Error Control

The new approach is a better estimate of error. Better time point selection.

– 160 dBc

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fREEDA, Transient Simulation and Frequency-Domain Modeling

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Three Milestones for Interfacing EM and Circuits • D. Winkelstein, M. B. Steer, and R. Pomerleau, “Simulation of arbitrary transmission line networks with nonlinear

terminations,” IEEE Trans. on Circuits and Systems, April 1991, pp.418-422. See also, IEEE Trans. on Circuits and Systems, Vol. 38, Oct. 1991.

• Impulse response and convolution • Time and frequency bounded

• C. S. Saunders, J. Hu, C. E. Christoffersen, and M. B. Steer, “Inverse singular value method for enforcing passivity in reduced-order models of distributed structures for transient and steady-state simulation,” IEEE Trans. Microwave Theory and Techniques, April 2011, pp. 837–847.

• S parameters to Foster Model • Passivity, causality

• C. S. Saunders and M. B. Steer, “Passivity enforcement for admittance models of distributed networks using an inverse eigenvalue method,” IEEE Transactions on Microwave Theory and Techniques, In Press.

• y parameters to Foster Model • Passivity, causality • What is needed for circuit simualtpors which are y parameter based

• ALL CONVERTERS NEED SOME HUERITIC KNOWLEDGE • Did the user provide sufficient data

• If not how to extrapolate • What is the basic response (what to emphasize)

• Low pass, Bandpass

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Approaches to Mixing EM Solvers

Frequency-Domain EM Solvers Produce a set of S parameters (or equivalent) Key-Problem is developing a causal/passive/accurate interface for

transient simulation The solution is the Foster Form with Appropriate Fitting Technique

Joining TD EM/ Circuits / FD EM Approach 1 Use fREEDA with FDTD interface and Foster Cannonical Form Interface

Approach 2 Build Foster Model into FDTD

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Workflow 31

EM Model In Frequency Domain Y(f)

Develop Foster N-Port

Time-Domain Circuit Simulation fREEDA

R. Mohan, J. C. Myoung, S. E. Mick, F. P. Hart, K. Chandrasekar, A. C. Cangellaris, P. D. Franzon and M. B. Steer, “Causal reduced-order modeling of distributed structures in a transient circuit simulator,” IEEE Trans. Microwave Theory and Tech, Vol. 52, No. 9, Sept. 2004, pp. 2207 – 2214.

In Review This is the most robust and accurate technique out there. Robustness is not perfect, heuristics required in extraction.

Main issue is in developing model that is 1) Causal 2) Passive 3) Accurate

Use to incorporate FD-EM in transient circuit simulator In xFDTD (not in current scope) but can join

xFDTD through fREEDA to EFD-EM solver

Either implement a Foster’s model directly or synthesize an R, L, C, K subcircuit.

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SINGARS SINGARS EM

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SINCGARS

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Output Waveforms

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Summary

• Most robust circuit simulator technology • Interfaces with TD and FD EM solvers. • Will be supported commercially. • fREEDA papers at

http://people.engr.ncsu.edu/mbs/Publications/mbs_publications.html

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